Finite Group Databasebeta

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D3×C19⋊C3×D55 #49178610

order37620
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD3×C19⋊C3×D55
unambiguous semidirect product(C5×D3)⋊(D11×C19⋊C3)
unambiguous semidirect product(D3×C11)⋊(D5×C19⋊C3)
unambiguous semidirect product(D3×C19×D55)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C19 ⋊ C22×C3
HallC3×C5×C11×C19⋊C3 ⋊ C22
HallC3×C11×C19⋊C3 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×C3×D3
HallC3×C5×C19⋊C3 ⋊ C2×D11
HallC11×C19 ⋊ C3×D3×D5
HallC3×C19⋊C3 ⋊ C2×D55
HallC5×C19 ⋊ C3×D3×D11
HallC5×C11 ⋊ C2×D3×C19⋊C3
SylowC19 ⋊ C3×D3×D55
SylowC11 ⋊ D3×D5×C19⋊C3
SylowC5 ⋊ D3×D11×C19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C19C22×C3
LCSG ▷ C3×C5×C11×C19
UCSC1

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

783 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 319);